Recurrence Relations
First-Order Recurrence Relations: ${a_n = sa_{n-1} + t}$ $a_n$ has this form: $a_n = c_1s^n+c_2$, $c_1, c_2$ solved by $$ a_0 = c_1+c_2\newline a_1 = c_1s+c_2 $$ Second-Order Recurrence Relations: ${a_n = s_1a_{n-1} + s_2a_{n-2}}$ Case 1: $x^2 - s_1x - s_2 = 0$ has 2 root $a_n$ has this form $a_n = c_1r_1^n+ c_2r_2^n$, where $r_1, r_2$ is the roots. $c_1, c_2$ solved by $$ a_0 = c_1+c_2 \newline a_1 = c_1r_1+ c_2r_2 $$...